Answer:
the solution of the system is x = 18/5 and y = 27/5.
Explanation:
To solve a system of equations using elimination, we can add or subtract the equations to eliminate one of the variables. In this case, we can add the given equations to eliminate the x-variable:
(-3x - 4y) + (x + y) = -54 + 15
-2x - 3y = -39
Dividing both sides by -3, we get:
(2/3)x + (1/3)y = 13/3
This equation tells us that x is equal to 2/3 times the value of y. Substituting this expression for x in one of the original equations, we can solve for y:
-3(2/3)y - 4y = -54
This simplifies to:
(-6/3)y - 4y = -54
Combining like terms, we get:
(-10/3)y = -54
Dividing both sides by -10/3, we get:
y = 27/5
Substituting this value for y in the expression for x, we get:
x = (2/3)(27/5) = 18/5
Therefore, the solution of the system is x = 18/5 and y = 27/5.